1.1 The Approximate Euclidean Shortest-path Problem
1.2 Approximating Minimum-Width Annuli and Shells
1.3 Approximating the Minimum-Volume Bounding Box
2.1 Notations
2.2 Approximating a Convex Polytope
2.3 Approximating Paths by a Outer Paths with Small Folding Angle
2.4 Projecting an Outer Path to a Polytope
2.5 Approximating the Diameter of a Point-Set
4.1 Introduction
4.2 Approximating a distance function by a weighted Voronoi diagram
4.3 Approximate Shortest-Path Map on a Polyhedral Surface in R^{3}
4.4 Constructing Spatial Approximate Shortest-Path Maps in R^{3}
4.5 Conclusions
5.1 Introduction
5.2 Geometric Preliminaries
5.3 A (1+eps)-Approximation Algorithm in Any
Dimension
5.3.1 A Strongly Polynomial eps-Approximation
Algorithm for the Minimum-Width Annulus in the Plane
9.1 Introduction
9.2 The Algorithm
9.3 Analysis of CompZoneOnline
9.3.1 Correctness
9.3.2 Running Time
9.4 Applications
9.4.1 Computing a Level in an Arrangement of Arcs
9.4.2 ther Applications
9.5 Conclusions
9.A Appendix - Pseudo-code for Subroutines of CompZoneOnline
9.B Appendix - Taking a Walk in Ten Easy Figures